Multigrid methods for elliptic problems: a review.

Abstract

Multigrid methods solve a large class of problems very efficiently. They work by approximating a problem on multiple overlapping grids with widely varying mesh sizes and cycling between these approximations, using relaxation to reduce the error on the scale of each grid. Problems solved by multigrid methods include general elliptic partial differential equations, nonlinear and eigenvalue problems, and systems of equations from fluid dynamics. The efficency is optimal: the computational work is proportional to the number of unknowns. This paper reviews the basic concepts and techniques of multigrid methods, concentrating on their role as fast solvers for eilliptic boundary-value problems.-from Authors